algorithms/leetcode/JavaScript/No239.sliding-window-maximum.js at master · ecmadao/algorithms · GitHub

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/**
 * Difficulty:
 * Hard
 *
 * Desc:
 * Given an array nums, there is a sliding window of size k which is moving from the very left of the array to the very right.
 * You can only see the k numbers in the window. Each time the sliding window moves right by one position.
 * Return the max sliding window.
 *
 * Example:
 * Input: nums = [1,3,-1,-3,5,3,6,7], and k = 3
 * Output: [3,3,5,5,6,7]
 * Explanation:
 * Window position                Max
 * ---------------               -----
 * [1  3  -1] -3  5  3  6  7       3
 * 1 [3  -1  -3] 5  3  6  7       3
 * 1  3 [-1  -3  5] 3  6  7       5
 * 1  3  -1 [-3  5  3] 6  7       5
 * 1  3  -1  -3 [5  3  6] 7       6
 * 1  3  -1  -3  5 [3  6  7]      7
 *
 * Note:
 * You may assume k is always valid, 1 ≤ k ≤ input array's size for non-empty array.
 *
 * Follow up:
 * Could you solve it in linear time?
 */

// =============================================== Solution 1 ===============================================

/**
  * @param {number[]} nums
  * @param {number} k
  * @return {number[]}
  *
  * 滑动窗口解法
  */
var maxSlidingWindow_1 = function(nums, k) {
  if (k <= 1) return nums

  const findMaxIndex = (start, end) => {
    let index = start
    let i = start + 1
    while (i <= end) {
      if (nums[i] >= nums[index]) {
        index = i
      }
      i += 1
    }
    return index
  }

  let i = 1
  let maxIndex = findMaxIndex(0, k - 1)
  const result = [nums[maxIndex]]

  while (i <= nums.length - k) {

    while (i <= maxIndex && i <= nums.length - k) {
      const lastIndex = i + k - 1
      const last = nums[lastIndex]
      if (last >= nums[maxIndex]) maxIndex = lastIndex
      result.push(nums[maxIndex])
      i += 1
    }

    maxIndex = findMaxIndex(i, i + k - 1)
  }

  return result
}

// =============================================== Solution 2 ===============================================

// 最大堆

class Heap {
  constructor() {
    this.queue = []
  }

  insert(val) {
    this.queue.push(val)
    this.sortWithFather(this.queue.length)
  }

  sortWithFather(index) {
    if (index < 2) return
    const fIndex = Math.floor(index / 2) - 1
    const tmp = this.queue[fIndex]
    if (tmp < this.queue[index - 1]) {
      this.queue[fIndex] = this.queue[index - 1]
      this.queue[index - 1] = tmp
    }
    this.sortWithFather(fIndex + 1)
  }

  peak() {
    if (!this.queue.length) return null
    return this.queue[0]
  }

  shift() {
    if (!this.queue.length) return null

    const result = this.queue.shift()
    if (!this.queue.length) return result
    const last = this.queue.pop()
    this.queue.unshift(last)
    this.sortWithChild(1)
    return result
  }

  sortWithChild(index) {
    const cIndex1 = index * 2 - 1
    if (cIndex1 > this.queue.length) return
    if (this.queue[index - 1] < this.queue[cIndex1]) {
      const tmp = this.queue[index - 1]
      this.queue[index - 1] = this.queue[cIndex1]
      this.queue[cIndex1] = tmp
    }

    const cIndex2 = index * 2
    if (cIndex2 > this.queue.length) return
    if (this.queue[index - 1] < this.queue[cIndex2]) {
      const tmp = this.queue[index - 1]
      this.queue[index - 1] = this.queue[cIndex2]
      this.queue[cIndex2] = tmp
    }

    this.sortWithChild(cIndex1 + 1)
    this.sortWithChild(cIndex2 + 1)
  }
}

/**
  * @param {number[]} nums
  * @param {number} k
  * @return {number[]}
  *
  * 最大堆解法
  */
var maxSlidingWindow_2 = function(nums, k) {
  if (!nums.length) return []
  if (k === 0) return []
  if (k === 1) return nums

  const heap = new Heap()
  const indexes = {}

  for (let i = 0; i < k; i += 1) {
    if (!indexes[nums[i]]) indexes[nums[i]] = []
    indexes[nums[i]].push(i)
    heap.insert(nums[i])
  }

  const result = [heap.peak()]

  for (let i = k; i < nums.length; i += 1) {
    const input = nums[i]
    if (!indexes[nums[i]]) indexes[nums[i]] = []
    indexes[nums[i]].push(i)
    heap.insert(input)

    while (heap.peak() !== null) {
      const peak = heap.peak()
      if (!indexes[peak] || !indexes[peak].length) {
        heap.shift()
      } else if (indexes[peak][0] <= i - k) {
        heap.shift()
        indexes[peak].shift()
      } else {
        result.push(peak)
        break
      }
    }
  }
  return result
}

// =============================================== Solution 3 ===============================================


/**
 * @param {number[]} nums
 * @param {number} k
 * @return {number[]}
 *
 * DP 动态规划
 * https://leetcode-cn.com/problems/sliding-window-maximum/solution/hua-dong-chuang-kou-zui-da-zhi-by-leetcode-3/
 */
var maxSlidingWindow_3 = function(nums, k) {
  if (!nums.length || !k) return []
  if (k === 1) return nums

  const left = []
  for (let i = 0; i < nums.length; i += 1) {
    if ((i + 1) % k === 0) {
      left[i] = nums[i]
    } else {
      left[i] = Math.max(left[i - 1], nums[i])
    }
  }
  const right = []
  for (let i = nums.length - 1; i >= 0; i -= 1) {
    if ((i + 1) % k === 0) {
      right[i] = nums[i]
    } else {
      right[i] = Math.max(right[i + 1], nums[i])
    }
  }

  const result = []
  for (let i = 0; i <= nums.length - k; i += 1) {
    result.push(
      Math.max(left[i + k - 1], right[i])
    )
  }
  return result
}

// =============================================== Solution 4 ===============================================

// 单调队列
class Deque {
  constructor() {
    this.deque = []
  }

  peak() {
    return this.deque[0]
  }

  push(val) {
    // 保证从左到右大小递减
    while (this.deque.length && this.deque.slice(-1)[0] < val) {
      this.deque.pop()
    }
    this.deque.push(val)
  }

  // 从顶部移除值。如果被移除的是最大值，则需要移除；否则对结果没有影响，无需移除
  shift(val) {
    if (this.deque.length && this.deque[0] === val) {
      this.deque.shift()
    }
  }
}

/**
  * @param {number[]} nums
  * @param {number} k
  * @return {number[]}
  *
  * 单调队列法：
  * https://mp.weixin.qq.com/s?__biz=MzAxODQxMDM0Mw==&mid=2247484506&amp;idx=1&amp;sn=fcaae7325b10905c808e085f8802b4eb&source=41#wechat_redirect
  */
var maxSlidingWindow_4 = function(nums, k) {
  if (!nums.length || !k) return []
  if (k === 1) return nums

  const result = []
  const deque = new Deque()
  for (let i = 0; i < nums.length; i += 1) {
    deque.push(nums[i])
    if (i >= k - 1) {
      i - k >= 0 && deque.shift(nums[i - k])
      result.push(deque.peak())
    }
  }
  return result
}


const nums = 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console.log(
  maxSlidingWindow_4(nums, 100)
)